Abstract

A self-contained approach to studying the unitary evolution of coupled qubits is introduced, capable of addressing a variety of physical systems described by exchange Hamiltonians containing Rabi terms. The method automatically determines both the Weyl chamber steering trajectory and the accompanying local rotations. Particular attention is paid to the case of anisotropic exchange with tracking controls, which is solved analytically. It is shown that, if computational subspace is well isolated, any exchange interaction can always generate high fidelity, single-step controlled-NOT (CNOT) logic, provided that both qubits can be individually manipulated. The results are then applied to superconductingqubit architectures, for which several CNOT gate implementations are identified. The paper concludes with consideration of two CNOT gate designs having high efficiency and operating with no significant leakage to higher-lying noncomputational states.

Received 10 July 2007Accepted 17 October 2007Published online 14 November 2007

Acknowledgments:

This work was supported by the Disruptive Technology Office under Grant No. W911NF-04-1-0204 and by the National Science Foundation under Grant No. CMS-0404031. The author thanks Michael Geller, John Martinis, Emily Pritchett, and Andrew Sornborger for useful discussions.